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Proc Natl Acad Sci U S A 2020 07 29;117(28):16431-16437. Epub 2020 Jun 29.

Josephine Bay Paul Center for Comparative Molecular Biology and Evolution, Marine Biological Laboratory, Woods Hole, MA 02543

Maternal effect senescence-a decline in offspring survival or fertility with maternal age-has been demonstrated in many taxa, including humans. Despite decades of phenotypic studies, questions remain about how maternal effect senescence impacts evolutionary fitness. To understand the influence of maternal effect senescence on population dynamics, fitness, and selection, we developed matrix population models in which individuals are jointly classified by age and maternal age. We fit these models to data from individual-based culture experiments on the aquatic invertebrate, (Rotifera). By comparing models with and without maternal effects, we found that maternal effect senescence significantly reduces fitness for and that this decrease arises primarily through reduced fertility, particularly at maternal ages corresponding to peak reproductive output. We also used the models to estimate selection gradients, which measure the strength of selection, in both high growth rate (laboratory) and two simulated low growth rate environments. In all environments, selection gradients on survival and fertility decrease with increasing age. They also decrease with increasing maternal age for late maternal ages, implying that maternal effect senescence can evolve through the same process as in Hamilton's theory of the evolution of age-related senescence. The models we developed are widely applicable to evaluate the fitness consequences of maternal effect senescence across species with diverse aging and fertility schedule phenotypes.

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http://dx.doi.org/10.1073/pnas.1919988117 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7368264 | PMC |

July 2020

Ecol Modell 2020 Feb;417:108856

Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, PO Box 94248, 1090 GE Amsterdam, The Netherlands.

Variance in life history outcomes among individuals is a requirement for natural selection, and a determinant of the ecological dynamics of populations. Heterogeneity among individuals will cause such variance, but so will the inherently stochastic nature of their demography. The relative contributions of these variance components - stochasticity and heterogeneity - to life history outcomes are presented here in a general, demographic calculation. A general formulation of sensitivity analysis is provided for the relationship between the variance components and the demographic rates within the life cycle. We illustrate these novel methods with two examples; the variance in longevity within and between frailty groups in a laboratory population of fruit flies, and the variance in lifetime reproductive output within and between initial environment states in a perennial herb in a stochastic fire environment. In fruit flies, an increase in mortality would increase the variance due to stochasticity and reduce that due to heterogeneity. In the plant example, increasing mortality reduces, and increasing fertility increases both variance components. Sensitivity analyses such as these can provide a powerful tool in identifying patterns among life history stages and heterogeneity groups and their contributions to variance in life history outcomes.

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http://dx.doi.org/10.1016/j.ecolmodel.2019.108856 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7015279 | PMC |

February 2020

Glob Chang Biol 2020 03 7;26(3):1170-1184. Epub 2019 Nov 7.

Centre d'Etudes Biologiques de Chizé, UMR 7372 du Centre National de la Recherche Scientifique-Université de La Rochelle, Villiers en Bois, France.

The Paris Agreement is a multinational initiative to combat climate change by keeping a global temperature increase in this century to 2°C above preindustrial levels while pursuing efforts to limit the increase to 1.5°C. Until recently, ensembles of coupled climate simulations producing temporal dynamics of climate en route to stable global mean temperature at 1.5 and 2°C above preindustrial levels were not available. Hence, the few studies that have assessed the ecological impact of the Paris Agreement used ad-hoc approaches. The development of new specific mitigation climate simulations now provides an unprecedented opportunity to inform ecological impact assessments. Here we project the dynamics of all known emperor penguin (Aptenodytes forsteri) colonies under new climate change scenarios meeting the Paris Agreement objectives using a climate-dependent-metapopulation model. Our model includes various dispersal behaviors so that penguins could modulate climate effects through movement and habitat selection. Under business-as-usual greenhouse gas emissions, we show that 80% of the colonies are projected to be quasiextinct by 2100, thus the total abundance of emperor penguins is projected to decline by at least 81% relative to its initial size, regardless of dispersal abilities. In contrast, if the Paris Agreement objectives are met, viable emperor penguin refuges will exist in Antarctica, and only 19% and 31% colonies are projected to be quasiextinct by 2100 under the Paris 1.5 and 2 climate scenarios respectively. As a result, the global population is projected to decline by at least by 31% under Paris 1.5 and 44% under Paris 2. However, population growth rates stabilize in 2060 such that the global population will be only declining at 0.07% under Paris 1.5 and 0.34% under Paris 2, thereby halting the global population decline. Hence, global climate policy has a larger capacity to safeguard the future of emperor penguins than their intrinsic dispersal abilities.

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http://dx.doi.org/10.1111/gcb.14864 | DOI Listing |

March 2020

Theor Popul Biol 2019 12 1;130:160-169. Epub 2019 Aug 1.

University of Amsterdam, Netherlands.

The outcome of natural selection depends on the demographic processes of birth, death, and development. Here, we derive conditions for protected polymorphism in a population characterized by age- or stage-dependent demography with two sexes. We do so using a novel two-sex matrix population model including basic Mendelian genetics (one locus, two alleles, random mating). Selection may operate on survival, growth, or fertility, any or all of which may differ between the sexes. The model can therefore incorporate genes with arbitrary pleiotropic and sex-specific effects. Conditions for protected polymorphism are expressed in terms of the eigenvalues of the linearization of the model at the homozygote boundary equilibria. We show that in the absence of sexual dimorphism, polymorphism requires heterozygote superiority in the genotypic population growth rate. In the presence of sexual dimorphism, however, heterozygote superiority is not required; an inferior heterozygote may invade, reducing the population growth rate and even leading to extinction (so-called evolutionary suicide). Our model makes no assumptions about separation of time scales between ecological and evolutionary processes, and can thus be used to project sex×stage×genotype dynamics of eco-evolutionary processes. Empirical evidence that sexual dimorphism affects extinction risk is growing, yet sex differences are often ignored in evolutionary demography and in eco-evolutionary models. Our analysis highlights the importance of sexual dimorphism and suggests mechanisms by which an allele can be favored by selection, yet drive a population to extinction, as a result of the structure and interdependence of sex- and stage-specific processes.

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http://dx.doi.org/10.1016/j.tpb.2019.07.012 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6892267 | PMC |

December 2019

BMJ Open 2019 03 30;9(3):e024952. Epub 2019 Mar 30.

Faculty of Science, University of Amsterdam, Amsterdam, The Netherlands.

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http://dx.doi.org/10.1136/bmjopen-2018-024952 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6475227 | PMC |

March 2019

Am Nat 2019 04 11;193(4):545-559. Epub 2019 Mar 11.

Demographic processes and ecological interactions are central to understanding evolution and vice versa. We present a novel framework that combines basic Mendelian genetics with the powerful demographic approach of matrix population models. The ecological components of the model may be stage classified or age classified, linear or nonlinear, time invariant or time varying, and deterministic or stochastic. Genotypes may affect, in fully pleiotropic fashion, any mixture of demographic traits (viability, fertility, development) at any points in the life cycle. The dynamics of the stage × genotype structure of the population are given by a nonlinear population projection matrix. We show how to construct this matrix and use it to derive sufficient conditions for a protected genetic polymorphism for the case of linear, time-independent demography. These conditions demonstrate that genotype-specific population growth rates (λ) do not determine the outcome of selection. Except in restrictive special cases, heterozygote superiority in λ is neither necessary nor sufficient for a genetic polymorphism. As a consequence, the population growth rate does not always increase, and populations can be driven to extinction due to evolutionary suicide. We demonstrate the construction and analysis of the model using data on a color polymorphism in the common buzzard (Buteo buteo). The model exhibits a stable genetic polymorphism and declining growth rate, consistent with field data and previous models.

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http://dx.doi.org/10.1086/701857 | DOI Listing |

April 2019

Ecol Appl 2019 04 4;29(3):e01855. Epub 2019 Mar 4.

Department of Biological Sciences, University of Alberta, Edmonton, Alberta , T6G 2E9, Canada.

Climate change is affecting species' distributions and abundances worldwide. Baseline population estimates, against which future observations may be compared, are necessary if we are to detect ecological change. Arctic sea ice ecosystems are changing rapidly and we lack baseline population estimates for many ice-associated species. Provided we can detect them, changes in Arctic marine ecosystems may be signaled by changes in indicator species such as ringed seals (Pusa hispida). Ringed seal monitoring has provided estimates of survival and fertility rates, but these have not been used for population-level inference. Using matrix population models, we synthesized existing demographic parameters to obtain estimates of historical ringed seal population growth and structure in Amundsen Gulf and Prince Albert Sound, Canada. We then formalized existing hypotheses about the effects of emerging environmental stressors (i.e., earlier spring ice breakup and reduced snow depth) on ringed seal pup survival. Coupling the demographic model to ice and snow forecasts available from the Coupled Model Intercomparison Project resulted in projections of ringed seal population size and structure up to the year 2100. These projections showed median declines in population size ranging from 50% to 99%. Corresponding to these projected declines were substantial changes in population structure, with increasing proportions of ringed seal pups and adults and declining proportions of juveniles. We explored if currently collected, harvest-based data could be used to detect the projected changes in population stage structure. Our model suggests that at a present sample size of 100 seals per year, the projected changes in stage structure would only be reliably detected by mid-century, even for the most extreme climate models. This modeling process revealed inconsistencies in existing estimates of ringed seal demographic rates. Mathematical population models such as these can contribute both to understanding past population trends as well as predicting future ones, both of which are necessary if we are to detect and interpret future observations.

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http://dx.doi.org/10.1002/eap.1855 | DOI Listing |

April 2019

Ecol Monogr 2018 Nov 11;88(4):560-584. Epub 2018 Jul 11.

Institute for Biodiversity and Ecosystem Dynamics University of Amsterdam Science Park 904 1098 XH Amsterdam The Netherlands.

This paper presents a comprehensive theory for the demographic analysis of populations in which individuals are classified by both age and stage. The earliest demographic models were age classified. Ecologists adopted methods developed by human demographers and used life tables to quantify survivorship and fertility of cohorts and the growth rates and structures of populations. Later, motivated by studies of plants and insects, matrix population models structured by size or stage were developed. The theory of these models has been extended to cover all the aspects of age-classified demography and more. It is a natural development to consider populations classified by both age and stage. A steady trickle of results has appeared since the 1960s, analyzing one or another aspect of age × stage-classified populations, in both ecology and human demography. Here, we use the vec-permutation formulation of multistate matrix population models to incorporate age- and stage-specific vital rates into demographic analysis. We present cohort results for the life table functions (survivorship, mortality, and fertility), the dynamics of intra-cohort selection, the statistics of longevity, the joint distribution of age and stage at death, and the statistics of life disparity. Combining transitions and fertility yields a complete set of population dynamic results, including population growth rates and structures, net reproductive rate, the statistics of lifetime reproduction, and measures of generation time. We present a complete analysis of a hypothetical model species, inspired by poecilogonous marine invertebrates that produce two kinds of larval offspring. Given the joint effects of age and stage, many familiar demographic results become multidimensional, so calculations of marginal and mixture distributions are an important tool. From an age-classified point of view, stage structure is a form of unobserved heterogeneity. From a stage-classified point of view, age structure is unobserved heterogeneity. In an age × stage-classified model, variance in demographic outcomes can be partitioned into contributions from both sources. Because these models are formulated as matrices, they are amenable to a complete sensitivity analysis. As more detailed and longer longitudinal studies are developed, age × stage-classified demography will become more common and more important.

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http://dx.doi.org/10.1002/ecm.1306 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6283253 | PMC |

November 2018

J Anim Ecol 2018 07;87(4):906-920

Biology Department, MS-50, Woods Hole Oceanographic Institution, Woods Hole, MA, USA.

Recent studies unravelled the effect of climate changes on populations through their impact on functional traits and demographic rates in terrestrial and freshwater ecosystems, but such understanding in marine ecosystems remains incomplete. Here, we evaluate the impact of the combined effects of climate and functional traits on population dynamics of a long-lived migratory seabird breeding in the southern ocean: the black-browed albatross (Thalassarche melanophris, BBA). We address the following prospective question: "Of all the changes in the climate and functional traits, which would produce the biggest impact on the BBA population growth rate?" We develop a structured matrix population model that includes the effect of climate and functional traits on the complete BBA life cycle. A detailed sensitivity analysis is conducted to understand the main pathway by which climate and functional trait changes affect the population growth rate. The population growth rate of BBA is driven by the combined effects of climate over various seasons and multiple functional traits with carry-over effects across seasons on demographic processes. Changes in sea surface temperature (SST) during late winter cause the biggest changes in the population growth rate, through their effect on juvenile survival. Adults appeared to respond to changes in winter climate conditions by adapting their migratory schedule rather than by modifying their at-sea foraging activity. However, the sensitivity of the population growth rate to SST affecting BBA migratory schedule is small. BBA foraging activity during the pre-breeding period has the biggest impact on population growth rate among functional traits. Finally, changes in SST during the breeding season have little effect on the population growth rate. These results highlight the importance of early life histories and carry-over effects of climate and functional traits on demographic rates across multiple seasons in population response to climate change. Robust conclusions about the roles of various phases of the life cycle and functional traits in population response to climate change rely on an understanding of the relationships of traits to demographic rates across the complete life cycle.

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http://dx.doi.org/10.1111/1365-2656.12827 | DOI Listing |

July 2018

Popul Health Metr 2018 06 7;16(1). Epub 2018 Jun 7.

Interdisciplinary Center on Research and Education on Population Dynamics (InCent), University of Southern Denmark, Campusvej 55, Odense, DK-5230, Denmark.

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http://dx.doi.org/10.1186/s12963-018-0165-5 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5992869 | PMC |

June 2018

Demography 2018 08;55(4):1585

University of Amsterdam, Amsterdam, the Netherlands.

We discovered an error in Eq. (12) (p. 1621).

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http://dx.doi.org/10.1007/s13524-018-0665-8 | DOI Listing |

August 2018

Proc Biol Sci 2018 03;285(1874)

Smithsonian Institution Forest Global Earth Observatory, Smithsonian Environmental Research Center, 647 Contees Wharf Road, Edgewater, MD 21307-0028, USA.

As population-level patterns of interest in forests emerge from individual vital rates, modelling forest dynamics requires making the link between the scales at which data are collected (individual stems) and the scales at which questions are asked (e.g. populations and communities). Structured population models (e.g. integral projection models (IPMs)) are useful tools for linking vital rates to population dynamics. However, the application of such models to forest trees remains challenging owing to features of tree life cycles, such as slow growth, long lifespan and lack of data on crucial ontogenic stages. We developed a survival model that accounts for size-dependent mortality and a growth model that characterizes individual heterogeneity. We integrated vital rate models into two types of population model; an analytically tractable form of IPM and an individual-based model (IBM) that is applied with stochastic simulations. We calculated longevities, passage times to, and occupancy time in, different life cycle stages, important metrics for understanding how demographic rates translate into patterns of forest turnover and carbon residence times. Here, we illustrate the methods for three tropical forest species with varying life-forms. Population dynamics from IPMs and IBMs matched a 34 year time series of data (albeit a snapshot of the life cycle for canopy trees) and highlight differences in life-history strategies between species. Specifically, the greater variation in growth rates within the two canopy species suggests an ability to respond to available resources, which in turn manifests as faster passage times and greater occupancy times in larger size classes. The framework presented here offers a novel and accessible approach to modelling the population dynamics of forest trees.

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http://dx.doi.org/10.1098/rspb.2017.2050 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5879618 | PMC |

March 2018

Theor Popul Biol 2018 03 31;120:62-77. Epub 2018 Jan 31.

Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Netherlands.

As an individual moves through its life cycle, it passes through a series of states (age classes, size classes, reproductive states, spatial locations, health statuses, etc.) before its eventual death. The occupancy time in a state is the time spent in that state over the individual's life. Depending on the life cycle description, the occupancy times describe different demographic variables, for example, lifetime breeding success, lifetime habitat utilisation, or healthy longevity. Models based on absorbing Markov chains provide a powerful framework for the analysis of occupancy times. Current theory, however, can completely analyse only the occupancy of single states, although the occupancy time in a set of states is often desired. For example, a range of sizes in a size-classified model, an age class in an age×stage model, and a group of locations in a spatial stage model are all sets of states. We present a new mathematical approach to absorbing Markov chains that extends the analysis of life histories by providing a comprehensive theory for the occupancy of arbitrary sets of states, and for other demographic variables related to these sets (e.g., reaching time, return time). We apply this approach to a matrix population model of the Southern Fulmar (Fulmarus glacialoides). The analysis of this model provides interesting insight into the lifetime number of breeding attempts of this species. Our new approach to absorbing Markov chains, and its implementation in matrix oriented software, makes the analysis of occupancy times more accessible to population ecologists, and directly applicable to any matrix population models.

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http://dx.doi.org/10.1016/j.tpb.2017.12.007 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5861321 | PMC |

March 2018

Theor Ecol 2018 8;11(2):129-140. Epub 2017 Dec 8.

Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Amsterdam, The Netherlands.

History matters when individual prior conditions contain important information about the fate of individuals. We present a general framework for demographic models which incorporates the effects of history on population dynamics. The framework incorporates prior condition into the -state variable and includes an algorithm for constructing the population projection matrix from information on current state dynamics as a function of prior condition. Three biologically motivated classes of prior condition are included: prior stages, linear functions of current and prior stages, and equivalence classes of prior stages. Taking advantage of the matrix formulation of the model, we show how to calculate sensitivity and elasticity of any demographic outcome. Prior condition effects are a source of inter-individual variation in vital rates, i.e., individual heterogeneity. As an example, we construct and analyze a second-order model of , a long-lived herb. We present population growth rate, the stable population distribution, the reproductive value vector, and the elasticity of to changes in the second-order transition rates. We quantify the contribution of prior conditions to the total heterogeneity in the stable population of using the entropy of the stable distribution.

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http://dx.doi.org/10.1007/s12080-017-0353-0 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6445492 | PMC |

December 2017

Popul Ecol 2018 28;60(1):89-99. Epub 2018 May 28.

Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands.

Variance in longevity among individuals may arise as an effect of heterogeneity (differences in mortality rates experienced at the same age or stage) or as an effect of individual stochasticity (the outcome of random demographic events during the life cycle). Decomposing the variance into components due to heterogeneity and stochasticity is crucial for evolutionary analyses.In this study, we analyze longevity from ten studies of invertebrates in the laboratory, and use the results to partition the variance in longevity into its components. To do so, we fit finite mixtures of Weibull survival functions to each data set by maximum likelihood, using the EM algorithm. We used the Bayesian Information Criterion to select the most well supported model. The results of the mixture analysis were used to construct an age × stage-classified matrix model, with heterogeneity groups as stages, from which we calculated the variance in longevity and its components. Almost all data sets revealed evidence of some degree of heterogeneity. The median contribution of unobserved heterogeneity to the total variance was 35%, with the remaining 65% due to stochasticity. The differences among groups in mean longevity were typically on the order of 30% of the overall life expectancy. There was considerable variation among data sets in both the magnitude of heterogeneity and the proportion of variance due to heterogeneity, but no clear patterns were apparent in relation to sex, taxon, or environmental conditions.

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http://dx.doi.org/10.1007/s10144-018-0616-7 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6435164 | PMC |

May 2018

Popul Ecol 2018 1;60(1):21-36. Epub 2018 Jun 1.

2Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, PO Box 94248, 1090 GE Amsterdam, The Netherlands.

Models of sexually-reproducing populations that consider only a single sex cannot capture the effects of sex-specific demographic differences and mate availability. We present a new framework for two-sex demographic models that implements and extends the birth-matrix mating-rule approach of Pollak. The model is a continuous-time matrix model that explicitly includes the processes of mating (which is nonlinear but homogeneous), offspring production, and demographic transitions and survival. The resulting nonlinear model converges to exponential growth with an equilibrium population composition. The model can incorporate age- or stage-structured life histories and flexible mating functions. As an example, we apply the model to analyze the effects of mating strategies (polygamy or monogamy, and mated unions composed of males and females, of variable duration) on the response to sex-biased harvesting. The combination of demographic complexity with the interaction of the sexes can have major population dynamic effects and can change the outcome of evolution on sex-related characters.

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http://dx.doi.org/10.1007/s10144-018-0615-8 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6435235 | PMC |

June 2018

J Anim Ecol 2018 Jan 10;87(1):212-222. Epub 2017 Oct 10.

Biology Department, Woods Hole Oceanographic Institution, Woods Hole, MA, USA.

Individuals are heterogeneous in many ways. Some of these differences are incorporated as individual states (e.g. age, size, breeding status) in population models. However, substantial amounts of heterogeneity may remain unaccounted for, due to unmeasurable genetic, maternal or environmental factors. Such unobserved heterogeneity (UH) affects the behaviour of heterogeneous cohorts via intra-cohort selection and contributes to inter-individual variance in demographic outcomes such as longevity and lifetime reproduction. Variance is also produced by individual stochasticity, due to random events in the life cycle of wild organisms, yet no study thus far has attempted to decompose the variance in demographic outcomes into contributions from UH and individual stochasticity for an animal population in the wild. We developed a stage-classified matrix population model for the southern fulmar breeding on Ile des Pétrels, Antarctica. We applied multievent, multistate mark-recapture methods to estimate a finite mixture model accounting for UH in all vital rates and Markov chain methods to calculate demographic outcomes. Finally, we partitioned the variance in demographic outcomes into contributions from UH and individual stochasticity. We identify three UH groups, differing substantially in longevity, lifetime reproductive output, age at first reproduction and in the proportion of the life spent in each reproductive state. -14% of individuals at fledging have a delayed but high probability of recruitment and extended reproductive life span. -67% of individuals are less likely to reach adulthood, recruit late and skip breeding often but have the highest adult survival rate. -19% of individuals recruit early and attempt to breed often. They are likely to raise their offspring successfully, but experience a relatively short life span. Unobserved heterogeneity only explains a small fraction of the variances in longevity (5.9%), age at first reproduction (3.7%) and lifetime reproduction (22%). UH can affect the entire life cycle, including survival, development and reproductive rates, with consequences over the lifetime of individuals and impacts on cohort dynamics. The respective role of UH vs. individual stochasticity varies greatly among demographic outcomes. We discuss the implication of our finding for the gradient of life-history strategies observed among species and argue that individual differences should be accounted for in demographic studies of wild populations.

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http://dx.doi.org/10.1111/1365-2656.12752 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5765524 | PMC |

January 2018

Ecotoxicology 2017 Aug 12;26(6):820-830. Epub 2017 May 12.

Department of Physics, University of Louisiana at Lafayette, Lafayette, LA, 70504-1010, USA.

Mathematical models are essential for combining data from multiple sources to quantify population endpoints. This is especially true for species, such as marine mammals, for which data on vital rates are difficult to obtain. Since the effects of an environmental disaster are not fixed, we develop time-varying (nonautonomous) matrix population models that account for the eventual recovery of the environment to the pre-disaster state. We use these models to investigate how lethal and sublethal impacts (in the form of reductions in the survival and fecundity, respectively) affect the population's recovery process. We explore two scenarios of the environmental recovery process and include the effect of demographic stochasticity. Our results provide insights into the relationship between the magnitude of the disaster, the duration of the disaster, and the probability that the population recovers to pre-disaster levels or a biologically relevant threshold level. To illustrate this modeling methodology, we provide an application to a sperm whale population. This application was motivated by the 2010 Deepwater Horizon oil rig explosion in the Gulf of Mexico that has impacted a wide variety of species populations including oysters, fish, corals, and whales.

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http://dx.doi.org/10.1007/s10646-017-1813-4 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5496980 | PMC |

August 2017

Evol Biol 2017 4;44(1):5-10. Epub 2016 May 4.

Max Planck Odense Center on the Biodemography of Aging, Odense, Denmark.

The evolution of senescence is often explained by arguing that, in nature, few individuals survive to be old and hence it is evolutionarily unimportant what happens to organisms when they are old. A corollary to this idea is that extrinsically imposed mortality, because it reduces the chance of surviving to be old, favors the evolution of senescence. We show that these ideas, although widespread, are incorrect. Selection leading to senescence does not depend directly on survival to old age, but on the shape of the stable age distribution, and we discuss the implications of this important distinction. We show that the selection gradient on mortality declines with age even in the hypothetical case of zero mortality, when survivorship does not decline. Changing the survivorship function by imposing age independent mortality has no affect on the selection gradients. A similar result exists for optimization models: age independent mortality does not change the optimal result. We propose an alternative, brief explanation for the decline of selection gradients, and hence the evolution of senescence.

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http://dx.doi.org/10.1007/s11692-016-9385-4 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5321711 | PMC |

May 2016

Theor Popul Biol 2017 04 18;114:107-116. Epub 2017 Jan 18.

University of Amsterdam, Netherlands; Woods Hole Oceanographic Institution, United States.

Inter-individual variance in longevity (or any other demographic outcome) may arise from heterogeneity or from individual stochasticity. Heterogeneity refers to differences among individuals in the demographic rates experienced at a given age or stage. Stochasticity refers to variation due to the random outcome of demographic rates applied to individuals with the same properties. The variance due to individual stochasticity can be calculated from a Markov chain description of the life cycle. The variance due to heterogeneity can be calculated from a multistate model that incorporates the heterogeneity. We show how to use this approach to decompose the variance in longevity into contributions from stochasticity and heterogeneous frailty for male and female cohorts from Sweden (1751-1899), France (1816-1903), and Italy (1872-1899), and also for a selection of period data for the same countries. Heterogeneity in mortality is described by the gamma-Gompertz-Makeham model, in which a gamma distributed "frailty" modifies a baseline Gompertz-Makeham mortality schedule. Model parameters were estimated by maximum likelihood for a range of starting ages. The estimates were used to construct an age×frailty-classified matrix model, from which we compute the variance of longevity and its components due to heterogeneous frailty and to individual stochasticity. The estimated fraction of the variance in longevity due to heterogeneous frailty (averaged over time) is less than 10% for all countries and for both sexes. These results suggest that most of the variance in human longevity arises from stochasticity, rather than from heterogeneous frailty.

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http://dx.doi.org/10.1016/j.tpb.2017.01.001 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5336383 | PMC |

April 2017

Theor Ecol 2017 17;10(3):355-374. Epub 2017 Apr 17.

Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, PO Box 94248, 1090 GE Amsterdam, The Netherlands.

Lifetime reproductive output (LRO) determines per-generation growth rates, establishes criteria for population growth or decline, and is an important component of fitness. Empirical measurements of LRO reveal high variance among individuals. This variance may result from genuine heterogeneity in individual properties, or from individual stochasticity, the outcome of probabilistic demographic events during the life cycle. To evaluate the extent of individual stochasticity requires the calculation of the statistics of LRO from a demographic model. Mean LRO is routinely calculated (as the net reproductive rate), but the calculation of variances has only recently received attention. Here, we present a complete, exact, analytical, closed-form solution for all the moments of LRO, for age- and stage-classified populations. Previous studies have relied on simulation, iterative solutions, or closed-form analytical solutions that capture only part of the sources of variance. We also present the sensitivity and elasticity of all of the statistics of LRO to parameters defining survival, stage transitions, and (st)age-specific fertility. Selection can operate on variance in LRO only if the variance results from genetic heterogeneity. The potential opportunity for selection is quantified by Crow's index , the ratio of the variance to the square of the mean. But variance due to individual stochasticity is only an opportunity for selection. In a comparison of a range of age-classified models for human populations, we find that proportional increases in mortality have very small effects on the mean and variance of LRO, but large positive effects on . Proportional increases in fertility increase both the mean and variance of LRO, but reduce . For a size-classified tree population, the elasticity of both mean and variance of LRO to stage-specific mortality are negative; the elasticities to stage-specific fertility are positive.

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http://dx.doi.org/10.1007/s12080-017-0335-2 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6979506 | PMC |

April 2017

Ecol Evol 2016 10 7;6(19):6855-6879. Epub 2016 Sep 7.

Biology Department MS-34 Woods Hole Oceanographic Institution Woods Hole Massachusetts 02543; Institute for Biodiversity and Ecosystem Dynamics University of Amsterdam Amsterdam The Netherlands.

Mothers that experience different individual or environmental conditions may produce different proportions of male to female offspring. The Trivers-Willard hypothesis, for instance, suggests that mothers with different qualities (size, health, etc.) will use different sex ratios if maternal quality differentially affects sex-specific reproductive success. Condition-dependent, or facultative, sex ratio strategies like these allow multiple sex ratios to coexist within a population. They also create complex population structure due to the presence of multiple maternal conditions. As a result, modeling facultative sex ratio evolution requires not only sex ratio strategies with multiple components, but also two-sex population models with explicit stage structure. To this end, we combine nonlinear, frequency-dependent matrix models and multidimensional adaptive dynamics to create a new framework for studying sex ratio evolution. We illustrate the applications of this framework with two case studies where the sex ratios depend one of two possible maternal conditions (age or quality). In these cases, we identify evolutionarily singular sex ratio strategies, find instances where one maternal condition produces exclusively male or female offspring, and show that sex ratio biases depend on the relative reproductive value ratios for each sex.

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http://dx.doi.org/10.1002/ece3.2202 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5139946 | PMC |

October 2016

Ecol Lett 2016 09 11;19(9):1023-31. Epub 2016 Jul 11.

Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Amsterdam, 1090 GE, The Netherlands.

Current understanding of life-history evolution and how demographic parameters contribute to population dynamics across species is largely based on assumptions of either constant environments or stationary environmental variation. Meanwhile, species are faced with non-stationary environmental conditions (changing mean, variance, or both) created by climate and landscape change. To close the gap between contemporary reality and demographic theory, we develop a set of transient life table response experiments (LTREs) for decomposing realised population growth rates into contributions from specific vital rates and components of population structure. Using transient LTREs in a theoretical framework, we reveal that established concepts in population biology will require revision because of reliance on approaches that do not address the influence of unstable population structure on population growth and mean fitness. Going forward, transient LTREs will enhance understanding of demography and improve the explanatory power of models used to understand ecological and evolutionary dynamics.

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http://dx.doi.org/10.1111/ele.12628 | DOI Listing |

September 2016

Ecol Evol 2016 03 9;6(5):1470-92. Epub 2016 Feb 9.

Biology Department MS-34 Woods Hole Oceanographic Institution Woods Hole MA 02543 USA; Institute for Biodiversity and Ecosystem Dynamics University of Amsterdam Amsterdam The Netherlands.

The evolution of the primary sex ratio, the proportion of male births in an individual's offspring production strategy, is a frequency-dependent process that selects against the more common sex. Because reproduction is shaped by the entire life cycle, sex ratio theory would benefit from explicitly two-sex models that include some form of life cycle structure. We present a demographic approach to sex ratio evolution that combines adaptive dynamics with nonlinear matrix population models. We also determine the evolutionary and convergence stability of singular strategies using matrix calculus. These methods allow the incorporation of any population structure, including multiple sexes and stages, into evolutionary projections. Using this framework, we compare how four different interpretations of sex-biased offspring costs affect sex ratio evolution. We find that demographic differences affect evolutionary outcomes and that, contrary to prior belief, sex-biased mortality after parental investment can bias the primary sex ratio (but not the corresponding reproductive value ratio). These results differ qualitatively from the widely held conclusions of previous models that neglect demographic structure.

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http://dx.doi.org/10.1002/ece3.1902 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4747320 | PMC |

March 2016

J Anim Ecol 2016 Mar 27;85(2):371-84. Epub 2016 Jan 27.

Laboratory of Evolutionary Biodemography Laboratory, Max Planck Institute for Demographic Research, Konrad-Zuse-Straße 1, Rostock, DE-18057, Germany.

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http://dx.doi.org/10.1111/1365-2656.12482 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4819704 | PMC |

March 2016

Methods Ecol Evol 2014 May 19;5(5):473-482. Epub 2014 May 19.

Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam Amsterdam, The Netherlands.

Second derivatives of the population growth rate measure the curvature of its response to demographic, physiological or environmental parameters. The second derivatives quantify the response of sensitivity results to perturbations, provide a classification of types of selection and provide one way to calculate sensitivities of the stochastic growth rate. Using matrix calculus, we derive the second derivatives of three population growth rate measures: the discrete-time growth rate λ, the continuous-time growth rate = log λ and the net reproductive rate , which measures per-generation growth. We present a suite of formulae for the second derivatives of each growth rate and show how to compute these derivatives with respect to projection matrix entries and to lower-level parameters affecting those matrix entries. We also illustrate several ecological and evolutionary applications for these second derivative calculations with a case study for the tropical herb .

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http://dx.doi.org/10.1111/2041-210X.12179 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4358155 | PMC |

May 2014

Demogr Res 2014 May;30:1367-1396

Hopkins Center for Population Aging and Health, Hopkins Population Center, and Department of Sociology, Johns Hopkins University, USA.

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http://dx.doi.org/10.4054/DemRes.2014.30.48 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4326020 | PMC |

May 2014

Ecol Appl 2013 Dec;23(8):1893-905

Biology Department MS-34, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA.

The population effects of harvest depend on complex interactions between density dependence, seasonality, stage structure, and management timing. Here we present a periodic nonlinear matrix population model that incorporates seasonal density dependence with stage-selective and seasonally selective harvest. To this model, we apply newly developed perturbation analyses to determine how population densities respond to changes in harvest and demographic parameters. We use the model to examine the effects of popular control strategies and demographic perturbations on the invasive weed garlic mustard (Alliaria petiolata). We find that seasonality is a major factor in harvest outcomes, because population dynamics may depend significantly on both the season of management and the season of observation. Strategies that reduce densities in one season can drive increases in another, with strategies giving positive sensitivities of density in the target seasons leading to compensatory effects that invasive species managers should avoid. Conversely, demographic parameters to which density is very elastic (e.g., seeding survival, second-year rosette spring survival, and the flowering to fruiting adult transition for maximum summer densities) may indicate promising management targets.

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http://dx.doi.org/10.1890/12-1712.1 | DOI Listing |

December 2013

Nature 2014 Jan 8;505(7482):169-73. Epub 2013 Dec 8.

1] Max-Planck Odense Center on the Biodemography of Aging, Campusvej 55, 5230 Odense M, Denmark [2] Max Planck Institute for Demographic Research, Konrad-Zuse-Strasse 1, 18057 Rostock, Germany [3] Duke Population Research Institute, Duke University, Durham, North Carolina 27705, USA.

Evolution drives, and is driven by, demography. A genotype moulds its phenotype's age patterns of mortality and fertility in an environment; these two patterns in turn determine the genotype's fitness in that environment. Hence, to understand the evolution of ageing, age patterns of mortality and reproduction need to be compared for species across the tree of life. However, few studies have done so and only for a limited range of taxa. Here we contrast standardized patterns over age for 11 mammals, 12 other vertebrates, 10 invertebrates, 12 vascular plants and a green alga. Although it has been predicted that evolution should inevitably lead to increasing mortality and declining fertility with age after maturity, there is great variation among these species, including increasing, constant, decreasing, humped and bowed trajectories for both long- and short-lived species. This diversity challenges theoreticians to develop broader perspectives on the evolution of ageing and empiricists to study the demography of more species.

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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4157354 | PMC |

http://dx.doi.org/10.1038/nature12789 | DOI Listing |

January 2014

Demography 2013 Oct;50(5):1615-40

Max Planck Institute for Demographic Research, Konrad-Zuse Str. 1, 18057, Rostock, Germany,

A number of indices exist to calculate lifespan variation, each with different underlying properties. Here, we present new formulae for the response of seven of these indices to changes in the underlying mortality schedule (life disparity, Gini coefficient, standard deviation, variance, Theil's index, mean logarithmic deviation, and interquartile range). We derive each of these indices from an absorbing Markov chain formulation of the life table, and use matrix calculus to obtain the sensitivity and the elasticity (i.e., the proportional sensitivity) to changes in age-specific mortality. Using empirical French and Russian male data, we compare the underlying sensitivities to mortality change under different mortality regimes to determine the conditions under which the indices might differ in their conclusions about the magnitude of lifespan variation. Finally, we demonstrate how the sensitivities can be used to decompose temporal changes in the indices into contributions of age-specific mortality changes. The result is an easily computable method for calculating the properties of this important class of longevity indices.

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http://dx.doi.org/10.1007/s13524-013-0223-3 | DOI Listing |

October 2013

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